On the deprojection of axisymmetric bodies

Axisymmetric density distributions are constructed which are invisible when viewed from a range of inclination angles i. By adding such distributions to a model galaxy, it can be made either discy or boxy without in any way affecting its projected image. As the inclination of a galaxy decreases from edge-on to face-on, the range of 'invisible' densities, the uncertainty in the deprojection, and the sensitivity of the deprojection to noise all increase. The relation between these phenomena is clarified by an analysis of Palmer's deprojection algorithm. These results imply that disc-to-bulge ratios are in principle ill-determined from photometry unless the disc is strong or the system is seen precisely edge-on. Further observational work should therefore concentrate on systems that are believed to be nearly edge-on. The uncertain role of third integrals in galaxies makes it unclear to what degree this indeterminacy can be resolved by kinematic studies.